Open AccessOn Multiquadric Shape Determining Strategies in Image Reconstruction Applications: A Comparative Study
Author(s) -
N Sriapai,
Pichapop Paewpolsong,
Dusita Ritthison,
Sayan Kaennakham
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2090/1/012147
Subject(s) - radial basis function , interpolation (computer graphics) , partial differential equation , computer science , mathematics , meshfree methods , shape parameter , image (mathematics) , function (biology) , key (lock) , artificial neural network , algorithm , mathematical optimization , machine learning , artificial intelligence , mathematical analysis , statistics , finite element method , physics , evolutionary biology , biology , thermodynamics , computer security
After being introduced to approximate two-dimensional geographical surfaces in 1971, the multivariate radial basis functions (RBFs) have been receiving a great amount of attention from scientists and engineers. Over decades, RBFs have been applied to a wide variety of problems. Approximation, interpolation, classification, prediction, and neural networks are inevitable in nowadays science, engineering, and medicine. Moreover, numerically solving partial differential equations (PDEs) is also a powerful branch of RBFs under the name of the ‘Meshfree/Meshless’ method. Amongst many, the so-called ‘Generalized Multiquadric (GMQ)’ is known as one of the most used forms of RBFs. It is of ( ɛ 2 + r 2 ) β form, where r = ║ x-x Θ ║ 2 for x, x Θ ∈ ℝ n represents the distance function. The key factor playing a very crucial role for MQ, or other forms of RBFs, is the so-called ‘shape parameter ɛ ’ where selecting a good one remains an open problem until now. This paper focuses on measuring the numerical effectiveness of various choices of ɛ proposed in literature when used in image reconstruction problems. Condition number of the interpolation matrix, CPU-time and storage, and accuracy are common criteria being utilized. The results of the work shall provide useful information on selecting a ‘suitable and reliable choice of MQ-shape’ for further applications in general.